Team games, hypergraph spaces, and projective Boolean algebras

DOI10.1016/J.TOPOL.2022.108291arXiv1607.07944MaRDI QIDQ6275970

Author name not available (Why is that?)

Publication date: 26 July 2016

Abstract: We modify the game Fuchino, Koppelberg, and Shelah used to characterize the $kappa$-Freese-Nation property for a given Boolean algebra $A$, replacing players I and II each with a team of $n$ players with limited information. We show that $A$ is tightly $kappa$-filtered exactly when team II has a winning strategy for every finite team size. Case $kappa=alep{h}_0$ characterizes projective Boolean algebras and, hence, Dugundji spaces. In terms of the open-open game of Daniels, Kunen, and Zhou, this characterization is a team version of very I-favorable. We similarly characterize Cohen algebras in terms of a team version of I-favorability. If $A$ is the clopen algebra of the space of $n$-uniform hypergraphs on $kapp{a}^{+n}$ that avoid copies of $[n+1{]}^n$, then team II has a winning strategy for our modified FKS game for team size $n-1$ but not $n$. For $ngeq3$, this algebra also answers a question of Geschke when combined with a locally $<kappa$-sized characterization of tightly $kappa$-filtered Boolean algebras that we prove. Case $kappa=alep{h}_0$ includes a locally finite characterization of projective Boolean algebras.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Team games, hypergraph spaces, and projective Boolean algebras

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6275970)